You can't restore your account here if you've changed your name since deleting it from the site. It counts the new name as deleted too and won't allow you to restore from the code from the old name or new name.
@BlindMango

They are not bound to any account until the account is synced through the trophy app on the vita. Until that point, they are on the vita's memory in a default or "blank" account as some people seem to be fixated on.
As for the method of the account switching, some seem to be fixated on the website's name that is linked in the op to send you the email. This can be done by literally anyone by emailing the line "URL:psnreg:" in an.ics file (a calendar file used by google calendar, outlook, apple calendar, and other leading calendar apps.) Due to a bug in the way the vita reads these .ics files, it can then access the vita's registry to unlock various hidden apps including the sign in app. Using the sign in app to change users then gets the vita to sync the "blank" account's trophies to the currently signed in account.
You are correct in saying that this is the same as earning trophies on a "blank" account on a ps3 or ps4. The only difference is that a bug needs to be exploited in order to sync these "blank" trophies to an account other than the one that purchased the game. Because some don't understand the method, they call it a CFW. If you'd like to save yourself a headache, I'd suggest that you stop entertaining the opinions of the misinformed.

Unless you've discovered an exploit that allows playing of professional difficulty before finishing the game, your save file was modified so that you could do so on the first time, modified after saving at the last typewriter so that the game thought it was on professional difficulty, or you deleted your trophy list after already completing the game once and unlocking professional difficulty. All three of these possibilities are flaggable on this site. If you can show repeatable steps to unlock professional difficulty prior to completing the game, your flag will be lifted.

I'm agreeing with MMDE in thinking that this is going to far and should be labeled cheating. It's not a simple DNS switch. It's more similar to the packet-intercepts that were used with Street Fighter V.
This is sly's official response to that one:

Enter the first part of the code then release the back touch pad. Press the back touch pad again and enter the second code. That's how i got it to work myself. It should make a noise if you're entered it in correctly.
On the vita I viewed each cutscene in scene viewer mode to get some of the trophies to unlock. For others I needed to replay the specific task in level select. To pick scene viewer/level select you will need to be on the main menu and pick secrets. Alternatively, you can press and hold L2 + R1 (top left part of the back touch pad + R) while on the pause menu in a mission. This shows the hidden menu options. Go to the secrets section from here and you'll be able to pick scene viewer/level select as well.
For the metal head gems, I killed the final boss from level select and then got to the post-game. Once in post-game I went to Mountain Temple (found through the hole in the city in the gardens) and went to the right path past the precursor platform that must be shot to pass. I followed this path until the ambush of weak metal heads appeared. I killed all of them and averaged about 30 gems each run. After killing them, I paused the game and selected restart mission. It put me back at the teleporter and I cycled through the metal heads again until I had 510 gems. The orbs can be obtained with the orb glitch. Each of these collectables needs to be manually obtained as there is no player 2 to press L3 + X to give you 1000 orbs and gems. Since this is the vita version, you can also use the secrets glitch to give yourself infinite dark jak, infinite ammo, and infinite health. That's detailed in this thread if you're unaware of how to use it.
On a side note, it seems random which trophies unlock by the scene viewer method. Another member of a discord server I'm on tried this on the vita version and he had different trophies unlock than I did.